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Lecture 1: Basic Terms and Rules in Mathematics Lecture 10: quantum physics, particle physics, Content: - quantum physics, further comments and info - Heisenberg's uncertainty principle - Copenhagen interpretation - Schrödinger‘s equation - orbital model of the atom - basic parameters of particles - particle physics, quarks - the Standard model quantum physics Quantum mechanics gradually arose from Max Planck's solution in 1900 and Albert Einstein's 1905 paper which offered a quantum-based theory to explain the photoelectric effect. Comment: Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself, but Einstein interpreted Planck's quantum hypothesis realistically. Early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. Important applications of quantum mechanical theory include superconducting magnets, light-emitting diodes and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy, and explanations for many biological and physical phenomena. quantum physics The foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wilhelm Wien, Satyendra Nath Bose, Arnold Sommerfeld, and others. The Copenhagen interpretation of Niels Bohr became widely accepted (we will come in more detail to it later), important was also the Fifth Solvay Conference in 1927. By 1930, quantum mechanics had been further unified and formalized by the work of David Hilbert, Paul Dirac and John von Neumann with greater emphasis on measurement, the statistical nature of our knowledge of reality, and philosophical speculation about the 'observer'. It has since permeated many disciplines including quantum chemistry, quantum electronics, quantum optics, and quantum information science. quantum physics – four classes of phenomena (1/4) Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller (< 10-10 m). Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: • quantization of certain physical properties, • quantum entanglement, • principle of uncertainty, • wave–particle duality. 1. Quantization: Quantization is a process of transition from a classical understanding of physical phenomena to an understanding known as "quantum mechanics". It converts classical fields into operators acting on quantum states of the field theory. There exist various methods of quantization (geometrical-, canonical-, loop-, path integral- quantization, etc....). quantum physics – four classes of phenomena (2/4) Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller (< 10-10 m). Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: • quantization of certain physical properties, • quantum entanglement, • principle of uncertainty, • wave–particle duality. 2. Quantum entanglement: Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently – instead, a quantum state must be described for the system as a whole. For example, if a pair of particles are generated in such a way that their total spin is known to be zero, and one particle is found to have clockwise spin on a certain axis, then the spin of the other particle, measured on the same axis, will be found to be counterclockwise, as to be expected due to their entanglement. This is connected with the so called EPR paradox (Einstein-Podolsky-Rosen paradox). We will come to it little bit later on. quantum physics – four classes of phenomena (3/4) Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller (< 10-10 m). Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: • quantization of certain physical properties, • quantum entanglement, • principle of uncertainty, • wave–particle duality. 3. Principle of uncertainty: Called also Heisenberg's uncertainty principle - is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known simultaneously. Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. Heisenberg's uncertainty principle: Later on it has been expressed in a form of following expression (with standard deviation of position x and stand. dev. of momentum p): Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. But it has been shown that the uncertainty principle is inherent in the properties of all wave-like systems and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. Hint: Let's say you want to find out where an electron is and where it is going. How would you do it? The very act of looking depends upon light, which is made of photons, and these photons could have enough momentum that once they hit the electron they would change its course! Heisenberg's uncertainty principle: W. Heisenberg wrote: "Of course the introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary here and cannot be omitted from the interpretation of quantum theory". Something more from N. Bohr : “ A quantum phenomenon is a process, a passage from initial to final condition, not an instantaneous "state" in the classical sense of that word.“ little bit from another kit: „Why turbulence?“ quantum physics – four classes of phenomena (4/4) Quantum mechanics is essential to understanding the behavior of systems at atomic length scales and smaller (< 10-10 m). Broadly speaking, quantum mechanics incorporates four classes of phenomena for which classical physics cannot account: • quantization of certain physical properties, • quantum entanglement, • principle of uncertainty, • wave–particle duality. 4. Wave–particle duality: Wave–particle duality is the concept that every elementary particle or quantic entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects. Although the use of the wave-particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved - there exist several interpretations in quantum mechanics. interesting video: https://www.youtube.com/watch?v=Xmq_FJd1oUQ quantum physics Interpretations of quantum mechanics deal with two problems: a) how to relate the mathematical formalism of quantum mechanics to empirical observations; and b) how to understand that relation in physical and metaphysical terms and in ordinary language. The Copenhagen interpretation is an expression of the meaning of quantum mechanics that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg. It remains one of the most commonly taught interpretations of quantum mechanics. According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured, and quantum mechanics can only predict the probabilities that measurements will produce certain results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement. This feature is known as wavefunction collapse. To read more: https://en.wikipedia.org/wiki/Copenhagen_interpretation other or alternative interpretations (short overview): https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics quantum physics Ideas to self-study topics: Effects, which can be explained by means of quantum mechanics principles: • tunneling effect • Compton - effect • Raman - effect • Zeeman – effect. tunneling effect: https://www.youtube.com/watch?v=K64Tv2mK5h4 https://www.youtube.com/watch?v=WPZLRtyvEqo
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